where \(m, a\) and \(F\) are the mass, the acceleration and the force
respectively. Knowing the dimensions of \(m\) (\(M\)) and \(a\)
(\(L T^{-2}\)), we will determine the dimension of \(F\); obviously we
will find that it is a force: \(M L T^{-2}\).

From there we will use the expression of the gravitational force between the
particle of mass \(m\) and the body of mass \(M\), at a distance
\(r\)

\[F = \frac{G m M}{r^2}\]

to determine the dimension of the Newton’s constant \(G\). The result
should be \(L^3 M^{-1} T^{-2}\).